Classical Yang-Baxter equation and the $A_{\infty}$-constraint

TL;DR

This paper links elliptic solutions of the classical Yang-Baxter equation to triple Massey products on elliptic curves, introduces an associative version with two spectral parameters, and explores its degenerations.

Contribution

It establishes a novel connection between elliptic solutions and Massey products, and introduces an associative version of the Yang-Baxter equation with new solutions.

Findings

Elliptic solutions derived from Massey products on elliptic curves

Construction of an associative Yang-Baxter equation with two spectral parameters

Analysis of degenerations of elliptic solutions

Abstract

We show that elliptic solutions of the classical Yang-Baxter equation can be obtained from triple Massey products on elliptic curve. We introduce the associative version of this equation which has two spectral parameters and construct its elliptic solutions. We also study some degenerations of these solutions.